In-plane and out-of plane failure of an ice sheet using peridynamics

When dealing with ice structure interaction modeling, such as designs for offshore structures/icebreakers or predicting ice cover's bearing capacity for transportation, it is essential to determine the most important failure modes of ice. Structural properties, ice material properties, ice-structure interaction processes, and ice sheet geometries have significant effect on failure modes. In this paper two most frequently observed failure modes are studied; splitting failure mode for in-plane failure of finite ice sheet and out-of-plane failure of semi-infinite ice sheet. Peridynamic theory was used to determine the load necessary for in-plane failure of a finite ice sheet. Moreover, the relationship between radial crack initiation load and measured out-of-plane failure load for a semi-infinite ice sheet is established. To achieve this, two peridynamic models are developed. First model is a 2 dimensional bond based peridynamic model of a plate with initial crack used for the in-plane case. Second model is based on a Mindlin plate resting on a Winkler elastic foundation formulation for out-of-plane case. Numerical results obtained using peridynamics are compared against experimental results and a good agreement between the two approaches is obtained confirming capability of peridynamics for predicting in-plane and out-of-plane failure of ice sheets

Influence of different types of small-size defects on propagation of macro-cracks in brittle materials

The presence of defects in the structure requires noticeable attention and understanding of fracture mechanisms in brittle materials has to be established. Defects in the form of holes, macro- and micro-cracks are the main interest of this paper. This work investigates the dual role of holes and micro-crack arrays on toughening and degradation mechanisms in concrete structures. An ordinary state-based peridynamics (PD) model is utilized to analyse the fracture problem at the micro-level. The application of PD shows its advantage in crack-hole, macro- and micro-crack interaction problems since PD can accurately predict the contribution of defects on structural behaviour. The study of the three-point bending problem with five types of holes existing in the structure showed the crack arrest phenomena at the hole boundary and the “attraction” of the crack to propagate towards the hole. For the study of the macro- and micro-cracks interaction problem, various cases of the micro-crack distribution and inclination angles are considered and validated with analytical studies. The PD quasi-static simulations show good agreement with analytical solutions. Moreover, PD dynamic solutions show the capability of PD to capture complex crack propagation paths. It is observed that the presence of micro-cracks and holes ahead of the main crack can suppress its further propagation as well as have an influence on the crack propagation direction. The numerical results demonstrate the efficiency of the PD modelling of multiple crack interaction problems

Model order reduction of linear peridynamic systems using static condensation

Static condensation is widely used as a model order reduction technique to reduce the computational effort and complexity of classical continuum-based computational models, such as finite-element models. Peridynamic theory is a nonlocal theory developed primarily to overcome the shortcoming of classical continuum-based models in handling discontinuous system responses. In this study, a model order reduction algorithm is developed based on the static condensation technique to reduce the order of peridynamic models. Numerical examples are considered to demonstrate the robustness of the proposed reduction algorithm in reproducing the static and dynamic response and the eigenresponse of the full peridynamic models

Peridynamic modeling of diffusion by using finite element analysis

Diffusion modeling is essential in understanding many physical phenomena such as heat transfer, moisture concentration, electrical conductivity, etc. In the presence of material and geometric discontinuities, and non-local effects, a non-local continuum approach, named as peridynamics, can be advantageous over the traditional local approaches. Peridynamics is based on integro-differential equations without including any spatial derivatives. In general, these equations are solved numerically by employing meshless discretization techniques. Although fundamentally different, commercial finite element software can be a suitable platform for peridynamic simulations which may result in several computational benefits. Hence, this study presents the peridynamic diffusion modeling and implementation procedure in a widely used commercial finite element analysis software, ANSYS. The accuracy and capability of this approach is demonstrated by considering several benchmark problems

Peridynamics for anti-plane shear and torsional deformations

A rod or beam is one of the most widely used members in engineering construction. Such members must be properly designed to resist the applied loads. When subjected to antiplane (longitudinal) shear and torsional loading, homogeneous, isotropic, and elastic materials are governed by the Laplace equation in two dimensions under the assumptions of classical continuum mechanics, and are considerably easier to solve than their three-dimensional counterparts. However, when using the finite element method in conjunction with linear elastic fracture mechanics, crack nucleation and its growth still pose computational challenges, even under such simple loading conditions. This difficulty is mainly due to the mathematical structure of its governing equations, which are based on the local classical continuum theory. However, the nonlocal peridynamic theory is free of these challenges because its governing equations do not contain any spatial derivatives of the displacement components, and thus are valid everywhere in the material. This study presents the peridynamic equation of motion for antiplane shear and torsional deformations, as well as the peridynamic material parameters. After establishing the validity of this equation, solutions for specific components that are weakened by deep edge cracks and internal cracks are presented

Nonlocal numerical simulation of low Reynolds number laminar fluid motion by using peridynamic differential operator

A considerable fluid load can cause local damages on the offshore structures, which may be a risk in the field of ocean engineering. Therefore, an accurate fluid motion prediction is a crucial issue in predicting the offshore structure motion. In this study, a non-local Lagrangian model is developed for Newtonian fluid low Reynold's number laminar flow. Based on the peridynamic theory, a peridynamic differential operator is recently proposed for directly converting the partial differential into its integral form. Therefore, the peridynamic differential operator is applied to convert the classical Navier-Stokes equations into their integral forms. The numerical algorithms are developed both in total and updated Lagrangian description. Finally, several benchmark fluid flow problems such as Couette flow, Poiseuille flow, Taylor Green vortex, shear-driven cavity problem and dam collapse problems are numerically solved. The simulation results are compared with the ones available in the published literature. The good agreements validate of the capability of the proposed non-local model for Newtonian fluid low Reynold's number laminar flow simulation